Shape keys and Drivers problem
To increase the effect of, and invert the direction that effects the shape key in your driver:


Go to File->User Preferences.
In the User Preferences window, select the File tab and check the box for "Auto Run Python Scripts".

Go to the graph editor in the Drivers tab and Change the type to "Scripted Expression".
In the expression box, type "-2 * var" (no quotes and with var being your variable name).



This expression will multiply the distance you target object travels by 2(or whatever you number you choose). So your target will have to move half as far. The higher the number, the shorter the distance. Making the number negative changes the direction it must travel. 

EDIT

After looking at the blend, the target is upside down on the Z axis, making its local space z axis(and your variable) -6.69. Negate that by adding 6.69 to it. Then multiply that by -10 so you will only have to move up by 0.1 to reach the maximum of the driver. So the expression is: -10 * (var + 6.69) And make sure "Auto Run Python Scripts" is enabled.